Locally finite varieties of Heyting algebras
type: Item
instance of: scholarly article
title: Locally finite varieties of Heyting algebras
zbMATH Open document ID: 1094.06009
author: Guram Bezhanishvili
author: R. Grigolia
published in: Algebra Universalis
publication date: 2006-03-21T00:00:00Z
review text: For a variety \(\mathcal V\) of Heyting algebras it is shown that the following are equivalent: (1) \(\mathcal V\) is locally finite; (2) the \(\mathcal V\)-coproduct of two finite \(\mathcal V\)-algebras is finite; (3) either \(\mathcal V\) is the variety of Boolean algebras or finite \(\mathcal V\)-copowers of the 3-element chain are finite. It is also shown that \(\mathcal V\) is generated by its finite members if and only if it is generated by a locally finite \(\mathcal V\)-algebra, and that \(\mathcal V\) is finitely generated if and only if it is residually finite.
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 03B55
zbMATH DE Number: 5013980
zbMATH Keywords: Heyting algebras
zbMATH Keywords: locally finite varieties
zbMATH Keywords: coproducts
MaRDI profile type: Publication
full work available at URL: s00012-005-1958-5
OpenAlex ID: W1995734546
DOI: 10.1007/S00012-005-1958-5
description: scientific article; zbMATH DE number 5013980